They don't. Sea-run cutthroat seldom move more than a few miles from the mouths of the rivers and streams where they spawn. In some of the larger rivers, some may never even leave the brackish water of the estuaries.

Fortunately, there are so many small creeks and streams that have populations of migrant coastal cutts that there are not many places in Puget Sound that don't have a few of them hanging around. March is the peak month for spawning, though it can take place anywhere from December through May, so most of the fish will have already spawned and returned to saltwater by now. Since cutthroat feed actively while on their spawning runs, they maintain their physical condition much better than steelhead, though I have caught the occasional "snake" who had apparently only recently returned to saltwater.

I've taken a few cutthroat at Lincoln Park at almost any time of the year, but have had more consistent fishing to the north. The beaches at Golden Gardens, Carkeek Park, Meadowdale Park and Picnic Point Park have all produced cutthroat (or salmon, or even Dolly Varden) well at one time of the year or another. Keep at it, you'll find 'em.